Questions: Lisa Honda is driving her car at high speed through a horizontal turn on a sharply banked roadway. Identify the free-body diagram that shows the type and direction of the forces acting on Lisa's car.

Solution Steps

Identify the forces acting on the car. These include:

• Gravitational force (\(mg\)) acting downward.
• Normal force (\(N\)) exerted by the road surface, acting perpendicular to the surface.
• Frictional force (\(f\)) which can act parallel to the surface, either up or down the bank, depending on the direction of the car's motion and the banking angle.

Determine the directions of these forces:

• Gravitational force (\(mg\)) acts vertically downward.
• Normal force (\(N\)) acts perpendicular to the banked surface, pointing away from the surface.
• Frictional force (\(f\)) acts parallel to the banked surface. If the car is moving too fast, friction acts up the bank to prevent slipping outward. If the car is moving too slow, friction acts down the bank to prevent slipping inward.

Draw the free-body diagram:

• Represent the car as a point.
• Draw an arrow downward from the point to represent the gravitational force (\(mg\)).
• Draw an arrow perpendicular to the banked surface to represent the normal force (\(N\)).
• Draw an arrow parallel to the banked surface to represent the frictional force (\(f\)), indicating the correct direction based on the car's speed and banking angle.

Final Answer